The present invention generally relates to a photometric stereoscopic shape measuring method. More particularly, the invention concerns a photometric stereoscopic shape measuring method which is capable of automatically correcting a reflectance map for assuring high accuracy for the stereoscopic measurement of a surface geometry of a specimen in a scanning electron microscope (hereinafter also referred to simply as SEM).
As a method of obtaining three dimensional information of an object, a stereoscopic measuring method has heretofore been adopted according to which corresponding points between two images picked up from two different points of sight are determined, wherein the three dimensional information is derived by processing appropriately the parallax errors. Effectiveness of such stereoscopic measurement is demonstrated in the preparation of topographical maps based on air photographs, by way of example. However, determination of the corresponding points between the two images involves a procedure which is time consuming. In the stereoscopic measurement of a specimen in an SEM, two images of the specimen are obtained by tilting a specimen table. At that time, manipulation such as readjustment of the focal point is required.
On the other hand, studies concerning acquisition of three-dimensional information have been intensively conducted in recent years from different standpoints. As a typical one, there may be mentioned a photometric stereoscopic shape measuring method. By way of example, this method is disclosed in K. Ikeuchi's article "Determining 3D Shape from 2D Shading Information Based on the Reflectance Map Technique" contained in "Periodical Collection of Articles" published by The Institute of Electronics and Communication Engineers of Japan, Vol. J65-D, No. 7 (1982/7), p.p. 842-849. As is discussed in this article, according to this photometric stereoscopic shape measuring method, an object under observation and the observation point are fixed in respect to their respective positions, wherein the direction in which the object is illuminated by a light source is varied to pick up a plurality of images. Since the positional relationship between the observation point and the object is fixed, the positional collation of the corresponding points usually required in the conventional stereoscopic measurements is rendered unnecessary. In in the case of the SEM, the direction in which a secondary electron detector is orientated coincides with the direction of illumination by the light sources in an optical system. Accordingly, by providing a plurality of detectors, it is possible to obtain a plurality of images simultaneously at one time.
The processing involved in carrying out the photometric stereoscopic shape measuring method may be generally classified into three steps, i.e. (a) inputting or loading of a plurality of images; (b) determination of inclinations of individual surface elements on the basis of brightness of individual picture elements or pixels of the images; and (c) determination of a stereoscopic shape through integration or the like processing of inclinations of the individual surface elements determined through the processing step (b). This processing will be described below in some detail.
FIG. 2 of the accompanying drawings shows a standard hardware arrangement for carrying out the photometric stereoscopic shape measurement. Referring to the figure, a reference numeral 1 denotes a camera for picking up the image of a specimen 6 supported on a specimen table 5 and adapted to be exchangeably illuminated by either one of light source 2, 3 or 4 at one time. In accordance with the commands inputted through a keyboard 8, a computer 7 turns on or off the light source 2, 3 or 4 and performs arithmetic operation on the information of three images supplied from the camera 1, which images are picked up by selectively turning on the light sources 2, 3 and 4, respectively, one by one. The surface shape or geometry of the specimen is thus obtained. A display 9 is adapted to display the results of the arithmetic operation or display the input images, as occasion requires. In the case of the most standard arrangement shown in FIG. 2, three light sources are employed. It should however be understood that four or more light sources may be used. Further, there is a special case in which only two light sources are employed. Besides, instead of employing a plurality of light sources, a single light source may be used, wherein the position of the light source can be varied, for example, by rotating the light source around the specimen. In any case, a common feature resides in that the positional relationship between the camera (i.e. observation point) and the specimen is fixed while the position(s) of the light source(s) is varied for picking up the images of specimen.
FIG. 3 of the accompanying drawings shows a hardware structure for the photometric stereoscopic shape measurement applied to a scanning electron microscope or SEM.
Referring to FIG. 3, an electron beam 19 emitted from an electron gun 11 disposed within a lens column 10 of the SEM at a top end thereof is caused to scan a surface of a specimen 17 on a specimen table 18 through an electronic lens system 12. As a result, secondary electrons (or information carriers such as reflected electrons) 20 are emitted from the specimen to be detected by detectors 13, 14, 15 and 16. A computer 21 performs arithmetic operation on the images obtained from the detection signals under the commands inputted through a keyboard 22, the results of the arithmetic operation being displayed on a display unit 23. Referring to FIG. 2 together with FIG. 3, it will be seen that the sight direction of the camera 1 shown in FIG. 2 corresponds to the direction of the electron beam 19 shown in FIG. 3, while the light sources 2, 3 and 4 correspond to the detectors 13, 14, 15 and 16 except that four detectors are shown in the arrangement of FIG. 3 because it is a common practice to use four detectors in most of the conventional SEMs. In the light of the correspondence existing between the systems shown in FIGS. 2 and 3 as mentioned above, the same principle validly applies to both systems. Accordingly, the following description will be made in conjunction with the hardware arrangement shown in FIG. 2, assuming that the arrangement of the SEM shown in FIG. 3 can be understood by the same description.
Now, a procedure of determining the directions or orientations of the individual surface elements will be described.
As is also discussed in Ikeuchi's article cited before, brightness in appearance of an object under observation is determined by the surface material or condition and three angles formed among the sight direction, the normal direction to the surface element and the illuminating direction of the light source. In this connection, it is noted that when the method of orthogonal projection can approximately apply valid and the distance between the light source and the object is sufficiently large as compared with the size of the object, the illuminating direction of the light source can be determined independent of spacial positions of surface elements of the object. In that case, brightness in appearance of the object can be determined when the orientations of the surface elements can be determined.
FIG. 4 is a view illustrating a Gaussian sphere 24 having a unit radius, an orthogonal coordinate system having x-axis 26, y-axis 27, z-axis 28 and the origin (O) 29, and a plane (.SIGMA.) 25 which contacts the Gaussian sphere 24 at a point defined by x=0, y=0 and z=1 and which can be expressed by an equation where z=1. When brightness in appearance at the individual points on the sphere 24 can be determined, brightness in appearance of the individual surface elements of the object under observation can be determined as the brightness of the points on the Gaussian sphere 24 having same inclinations or orientations as those of the surface elements on the conditions assumed above. In this ccnnection, a method of gnomonic or central projection is widely adopted according to which the spherical surface is projected to the plane (.SIGMA.) 25 with the origin (O) 29 serving as the point of sight. The result thus obtained through the central projection is referred to as the reflectance map. With the arrangement shown in FIG. 2, successive illumination of the semispherical specimen 6 of substantially Gaussian geometry, successive energization of the three light sources 2, 3 and 4 each at one time will result in three images 30, 31 and 32 shown schematically in FIGS. 5A, 5B and 5C, respectively. Referring to FIGS. 6A, 6B and 6C, the p-axis and q-axis denoted by numerals 36 and 37, respectively, are axes lying in the plane (.SIGMA.) 25 shown in FIG. 4, wherein the values or coordinates along the p-axis and q-axis represent inclination or orientation in the x- and y-axis directions of a corresponding point on the spherical surface 24 projected to the plane (.SIGMA.) 25 through the gnomonic or central projection. Consequently, a value on the reflectance map will represent the brightness of a surface element having a certain inclination or orientation. The reflectance maps corresponding to the images 30, 31 and 32 shown in FIGS. 5A, 5B and 5C are such as those shown in FIGS. 6A, 6B and 6C and designated by numerals 33, 34 and 35, respectively. As will be seen from FIGS. 6A, 6B and 6C, the reflectance map can be represented by equi-brightness contour lines (i.e. lines each interconnecting the points of same brightness) plotted about the point having the highest brightness. Assuming that brightnesses of same or corresponding points in three images of a specimen having a given shape and taken by the arrangement shown in FIG. 2 are represented by E.sub.1, E.sub.2 and E.sub.3, respectively, these brightnesses can be represented by the corresponding equi-brightness contour lines in the respective reflectance maps. These three equi-brightness contour lines plotted on a single reflectance map are then such as illustrated in FIG. 7. In the ideal case, the three equi-brightness contour lines intersect with one another at one point, whereby the direction or orientation of the surface elements under consideration can be determined. In this way, when the directions or orientations of all the surface elements can be determined, this means that the surface shape or geometry of the specimen can be determined through integration or the like processing.
It will now be understood from the above description in what manner the reflectance map is prepared by the photometric stereoscopic shape measuring method. Although the reflectance map is derived theoretically, a reflectance map prepared from the actual measurement of a typical or standard sample is also prepared for use for calibration. However, the reflectance map is very susceptible to the influence of insignificant variations in the observing conditions, difference in material of the specimen and the like variables. In the hitherto known photometric stereoscopic shape measuring method, no consideration is paid to this problem, as a result of which the result of measurement is often necessarily inaccurate.